Mostly due to political stability during critical periods in history. All regions of the world went through cycles of centralization and decentralization, and at various times might be considered 'more powerful' than the other. You've heard about all of the Arab contributions to science or how the Chinese invented everything first. These reflect times when Europe was in the dark ages and these areas were under strong, centralized governments that provided long term stability.
It just so happens that Europe was on one end of the cycle, and China and Arab nations on the other, during this time. So Europe was able to strongarm the Ottomans, the Chinese, everyone else, strengthening themselves even more and thus being able to hold an even firmer grip on these other regions.
I'd say Europe, Russia, China, and the Arabs all had an equal shot at what ended up going mostly to Britain and France.